Simplified Kalman filter for online rating: one-fits-all approach
This work provides a unified framework for online rating algorithms in sports, which is incremental as it generalizes existing methods.
The authors tackled the problem of online rating in sports by proposing a generic Bayesian approach that approximates a Kalman filter, applicable to any skills-outcome model and both individual and group sports, showing that well-known algorithms like Elo, Glicko, and TrueSkill are instances of their method.
In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new game by exploiting the probabilistic models of the relationship between the skills and the game outcome. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual -- as well as in the group-sports. We show how the well-know algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the one-fits-all approach we propose. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using the synthetic as well as the empirical data.